1. Field of the Invention
The present invention relates to interferometry. More particularly, the invention relates to methods and apparatus for rapid measurement of the optical phase-difference between two wavefronts. The invention may be implemented in optical systems that measure various parameters of test objects by generating test and reference waves having orthogonal polarizations.
2. Description of the Related Art
Phase-shift interferometry is an established method for measuring a variety of physical parameters ranging from the density of gases to the displacement of solid objects. An interferometric wavefront sensor employing phase-shift interferometry typically consists of a light source that is split into two wavefronts, a reference and a test wavefront, that are later recombined after traveling different path lengths. The relative phase difference between the two wavefronts is manifested as a two-dimensional intensity pattern known as an interferogram. Phase-shift interferometers typically have an element in the path of the reference or the test wavefront to introduce three or more known phase steps or phase shifts. By detecting the intensity pattern with a detector at each of the phase shifts, the phase distribution of the object wavefront can be calculated quantitatively and rapidly independently of the relative energy in the reference or object wavefronts.
Phase shifting of a light beam can either be accomplished by sequentially introducing a phase step (temporal phase shifting) or by splitting the beam into parallel channels for simultaneous phase steps (spatial phase shifting). Spatial phase shifting achieves data acquisition in a time several orders of magnitude smaller than temporal phase shifting, thus offering significant immunity to vibration.
Several methods of spatial phase shifting have been disclosed in the prior art. Smythe and Moore (1983) described a spatial phase-shifting method where conventional beam splitters and polarization optics are used to produce three or four phase-shifted images onto as many cameras for simultaneous detection. Several U.S. Patents [U.S. Pat. No. 4,575,248 (1986), U.S. Pat. No. 4,624,569 (1986), U.S. Pat. No. 5,589,938 (1996), No. 5,663,793 (1997), No. 5,777,741 (1998), and No. 5,883,717 (1999)] later disclosed variations of this approach wherein multiple cameras are used to detect multiple interferograms. These methods all require relatively complex optical and electronic arrangements.
Several publications describe methods that employ diffractive elements to simultaneously image three or more interferograms onto a single sensor. [See, for example, B. Barrientos et. al., “Transient Deformation Measurement with ESPI Using a Diffractive Optical Element for Spatial Phase-stepping,” Fringe, Akademie Verlag (1997): 317-8; A. Hettwer, “Three Channel Phase-Shifting Interferometer Using Polarization-Optics and a Diffraction Grating,” Optical Engineering, pp. 960, Vol. 39 No. 4, April 2000; and U.S. Pat. No. 4,624,569 (1986), No. 6,304,330 (2001) and No. 6,522,808 (2003).] While these methods are more compact and less expensive than multi-camera arrangements, they operate only over a limited wavelength range due to dispersion and chromatic distortion inherent in their design. Thus, they are not capable of working with white light or short coherence-length source interferometers. The Mireau interferometer configuration is particularly difficult to implement using the techniques of the prior-art [such as disclosed in U.S. Pat. Nos. 5,166,751 and 5,953,124, and in Ngoi, B. K. A., Venkatakrishnan, K., and Sivakumar, N. R., “Phase-shifting Interferometery Immune to Vibration,” Applied Optics, Vol. 40, No. 19, P. 3211 (2001)].
Spatial phase shifting has also been accomplished using a tilted reference wave to induce a spatial carrier frequency to the pattern. See, for example, U.S. Pat. No. 5,155,363 (1992) and No. 5,361,312 (1994). The spatial carrier method inherently requires a path-length difference of many hundreds of waves between the test and reference wavefronts, thereby precluding the use of white light. In addition, interferometers employing this arrangement must utilize high precision optics to avoid introducing aberrations between the two non-common path beams. U.S. Pat. No. 4,872,755 (1989) teaches the use of a short coherence-length source in combination with a Fizeau-type interferometer to effect instantaneous phase measurement with either the four camera arrangement of Symthe et. al. or a tilted carrier wave.
The prior art also describes the fabrication of micropolarizer arrays where each element has a different polarizer orientation in a repeating pattern. In particular, U.S. Pat. No. 5,327,285 and No. 6,384,971 describe the fabrication of micropolarizer arrays using multiple film layers for use in stereoscopic viewing. Nordin et al. describe the use of micropolarizer arrays made from fine conducting wire arrays for imaging polarimetry in the near infrared spectrum (“Micropolarizer Array for Infrared Imaging Polarimetry,” J. Opt. Soc. Am A, Vol. 16, No. 5, 1999). Recently, the use of wire grid arrays has also been demonstrated in the visible region of the spectrum (see U.S. Pat. No. 6,108,131, No. 6,122,103, No. 6,208,463 and No. 6,243,199). The planar nature of the conducting strip structure permits using it as a polarizer over an extremely wide incident angle, including zero degrees, and over a broad range of wavelengths, provided the period remains much less than the wavelength. Other investigators (J. Gou et. al., “Fabrication of Thin-Film Micropolarizer Arrays for Visible Imaging Polarimetry,” Applied Optics, Vol. 39, No. 10, 2000) also describe the use of patterned multi-level organic thin films for imaging polarimetry in the visible spectral range.
This disclosure describes how a linear-carrier phase-mask can be used as an interferometer to measure optical path-length differences at high-speed, with a single detector array and over a broad wavelength range. A novel way of implementing Fizeau and Mirau polarization interferometers is also described.